Early forecasts of the effect in London of the government's squeeze on housing benefit concentrated on the numbers of households likely to have to move as a result. But when the policy was introduced two years ago a highly experienced housing activist told me to expect a lot of hard-up families to make substantial sacrifices in order to stay put. A recent report for the Department for Work and Pensions on the initial impacts of the policy draws out this often neglected point.

"There is evidence that households are 'holding on' to their current tenancies where possible," it says in relation to central London where the changes are hitting hardest, not least because of "the paucity of alternative affordable accommodation in these localities." In a chapter based on interviews with housing advisers about the worries tenants have they quote one from Westminster:

Absolute complete horror and disbelief in the fact that they might have to leave their local area. Ordinarily, if something had happened, like your landlord evicted you three years ago, you'd just move a few streets down, you could stay in your local area. But because there's no private rented accommodation and because temporary accommodation isn't really available, the choice is you can take your four kids and move into a bed and breakfast in Westminster or you can go out of borough and have a self-contained private flat - but it'll be in east London.

The report says that such advisers "sometimes struggled to understand claimants' strong desire to remain in the area in the face of such difficult accommodation circumstances," which could include putting up with worse conditions, overcrowding and getting into rent arrears.

Why is this "attachment to place" so strong? Again an insight came from Westminster:

A lot of people who I work with, because they don't use the Tube, have no understanding of London's geography...their lives are very small, they live between their home, the mosque, the school, the community centre, the supermarket, literally that is it...they live in very, very small pockets and have these very closely knit communities. Women on the estate will come and look after their kids and you have that support network.

The same sort of story has emerged from research on social housing tenants in Southwark, with deep anxiety expressed at the idea of having to make a move even to another part of the same borough.

Close neighbourhood ties with family, friends, employment options and, in some cases, places of worship are vital to poor households' sense of security. No wonder many are prepared to cut back on other expenditure - heat, light, clothing, food - in order to bridge shortfalls caused by reduced LHA payments, and cling hold of what they have for as long as they can.

This picture is at odds with the government's defence of its benefit cuts programme, which has so sneakily fed the charming myth that large, feckless families are fiddling the system and blowing the takings on luxury cruises and Lamborghinis (it is, remember, landlords who ultimately receive housing benefit, not those of their tenants who are hard-up enough to qualify for it).

The report also challenges the assertions of Boris Johnson and his more bumptious media chums that early predictions of substantial numbers of claimant households having to move were baseless.

The research was mostly done in the first half of last year - after the measures were introduced but before having an effect on existing claimants. It found a consensus among the London housing advisers it interviewed - from Westminster, Hackney, Brent and Barking and Dagenham - that, by the time the measures had come fully into force and the "blunting" effect of transitional measures had worn off, "evictions and homelessness would increase, that a significant number of households would have to relocate, and that the quality of accommodation on offer would continue to decline at the lower end of the private rented sector."